VSEPR theory
Valence shell electron pair repulsion theory, or VSEPR theory, is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. It is also named the Gillespie-Nyholm theory after its two main developers, Ronald Gillespie and Ronald Nyholm.
The premise of VSEPR is that the valence electron pairs surrounding an atom tend to repel each other and will, therefore, adopt an arrangement that minimizes this repulsion. This in turn decreases the molecule's energy and increases its stability, which determines the molecular geometry. Gillespie has emphasized that the electron-electron repulsion due to the Pauli exclusion principle is more important in determining molecular geometry than the electrostatic repulsion.
VSEPR theory is based on observable electron density rather than mathematical wave functions and hence unrelated to orbital hybridisation, although both address molecular shape. VSEPR has a physical basis in quantum chemical topology methods such as the electron localization function and the quantum theory of atoms in molecules.
History
The idea of a correlation between molecular geometry and number of valence electron pairs was originally proposed in 1939 by Ryutaro Tsuchida in Japan, and was independently presented in a Bakerian Lecture in 1940 by Nevil Sidgwick and Herbert Powell of the University of Oxford. In 1957, Ronald Gillespie and Ronald Sydney Nyholm of University College London refined this concept into a more detailed theory, capable of choosing between various alternative geometries.Overview
VSEPR theory is used to predict the arrangement of electron pairs around non-hydrogen atoms in molecules, especially simple and symmetric molecules, where these key, central atoms participate in bonding to two or more other atoms; the geometry of these key atoms and their non-bonding electron pairs in turn determine the geometry of the larger whole.The number of electron pairs in the valence shell of a central atom is determined after drawing the Lewis structure of the molecule, and expanding it to show all bonding groups and lone pairs of electrons. In VSEPR theory, a double bond or triple bond is treated as a single bonding group. The sum of the number of atoms bonded to a central atom and the number of lone pairs formed by its nonbonding valence electrons is known as the central atom's steric number.
The electron pairs are assumed to lie on the surface of a sphere centered on the central atom and tend to occupy positions that minimize their mutual repulsions by maximizing the distance between them. The number of electron pairs, therefore, determines the overall geometry that they will adopt. For example, when there are two electron pairs surrounding the central atom, their mutual repulsion is minimal when they lie at opposite poles of the sphere. Therefore, the central atom is predicted to adopt a linear geometry. If there are 3 electron pairs surrounding the central atom, their repulsion is minimized by placing them at the vertices of an equilateral triangle centered on the atom. Therefore, the predicted geometry is trigonal. Likewise, for 4 electron pairs, the optimal arrangement is tetrahedral.
Degree of repulsion
The overall geometry is further refined by distinguishing between bonding and nonbonding electron pairs. The bonding electron pair shared in a sigma bond with an adjacent atom lies further from the central atom than a nonbonding pair of that atom, which is held close to its positively charged nucleus. VSEPR theory therefore views repulsion by the lone pair to be greater than the repulsion by a bonding pair. As such, when a molecule has 2 interactions with different degrees of repulsion, VSEPR theory predicts the structure where lone pairs occupy positions that allow them to experience less repulsion. Lone pair–lone pair repulsions are considered stronger than lone pair–bonding pair repulsions, which in turn are considered stronger than bonding pair–bonding pair repulsions, distinctions that then guide decisions about overall geometry when 2 or more non-equivalent positions are possible. For instance, when 5 valence electron pairs surround a central atom, they adopt a trigonal bipyramidal molecular geometry with two collinear axial positions and three equatorial positions. An electron pair in an axial position has three close equatorial neighbors only 90° away and a fourth much farther at 180°, while an equatorial electron pair has only two adjacent pairs at 90° and two at 120°. The repulsion from the close neighbors at 90° is more important, so that the axial positions experience more repulsion than the equatorial positions; hence, when there are lone pairs, they tend to occupy equatorial positions as shown in the diagrams of the next section for steric number five.The difference between lone pairs and bonding pairs may also be used to rationalize deviations from idealized geometries. For example, the H2O molecule has four electron pairs in its valence shell: two lone pairs and two bond pairs. The four electron pairs are spread so as to point roughly towards the apices of a tetrahedron. However, the bond angle between the two O–H bonds is only 104.5°, rather than the 109.5° of a regular tetrahedron, because the two lone pairs exert a greater mutual repulsion than the two bond pairs.
A bond of higher bond order also exerts greater repulsion since the pi bond electrons contribute. For example in isobutylene, 2C=CH2, the H3C−C=C angle is larger than the H3C−C−CH3 angle. However, in the carbonate ion,, all three C−O bonds are equivalent with angles of 120° due to resonance.
AXE method
The "AXE method" of electron counting is commonly used when applying the VSEPR theory. The electron pairs around a central atom are represented by a formula AXnEm, where A represents the central atom and always has an implied subscript one. Each X represents a ligand. Each E represents a lone pair of electrons on the central atom. The total number of X and E is known as the steric number. For example in a molecule AX3E2, the atom A has a steric number of 5.Based on the steric number and distribution of Xs and Es, VSEPR theory makes the predictions in the following tables. Note that the geometries are named according to the atomic positions only and not the electron arrangement. For example, the description of AX2E1 as a bent molecule means that the three atoms AX2 are not in one straight line, although the lone pair helps to determine the geometry.
| Steric number | Molecular geometry 0 lone pairs | Molecular geometry 1 lone pair | Molecular geometry 2 lone pairs | Molecular geometry 3 lone pairs |
| 2 | | |||
| 3 | | | ||
| 4 | | | | |
| 5 | | | | |
| 6 | | | | |
| 7 | | | | |
| 8 | ||||
| 9 | Tricapped trigonal prismatic |
| Molecule type | Shape | Electron arrangement including lone pairs, shown in pale yellow | Geometry excluding lone pairs | Examples |
| AX2E0 | Linear | BeCl2, HgCl2, CO2 | ||
| AX2E1 | Bent | nitrite|, SO2, O3, CCl2 | ||
| AX2E2 | Bent | H2O, OF2 | ||
| AX2E3 | Linear | XeF2, triiodide|, XeCl2 | ||
| AX3E0 | Trigonal planar | BF3, carbonate|, nitrate|, SO3 | ||
| AX3E1 | Trigonal pyramidal | NH3, PCl3 | ||
| AX3E2 | T-shaped | ClF3, BrF3 | ||
| AX4E0 | Tetrahedral | CH4, phosphate|, sulfate|, perchlorate|, XeO4 | ||
| AX4E1 | Seesaw or disphenoidal | SF4 | ||
| AX4E2 | Square planar | XeF4 | ||
| AX5E0 | Trigonal bipyramidal | PCl5 | ||
| AX5E1 | Square pyramidal | ClF5, BrF5, XeOF4 | ||
| AX5E2 | Pentagonal planar | Tetramethylammonium pentafluoroxenate| | ||
| AX6E0 | Octahedral | SF6, WCl6 | ||
| AX6E1 | Pentagonal pyramidal | , | ||
| AX7E0 | Pentagonal bipyramidal | IF7 | ||
| AX8E0 | Square antiprismatic | ,, | ||
| AX9E0 | Tricapped trigonal prismatic | Potassium nonahydridorhenate| |
When the substituent atoms are not all the same, the geometry is still approximately valid, but the bond angles may be slightly different from the ones where all the outside atoms are the same. For example, the double-bond carbons in alkenes like C2H4 are AX3E0, but the bond angles are not all exactly 120°. Likewise, SOCl2 is AX3E1, but because the X substituents are not identical, the X–A–X angles are not all equal.
As a tool in predicting the geometry adopted with a given number of electron pairs, an often used physical demonstration of the principle of minimal electron pair repulsion utilizes inflated balloons. Through handling, balloons acquire a slight surface electrostatic charge that results in the adoption of roughly the same geometries when they are tied together at their stems as the corresponding number of electron pairs. For example, five balloons tied together adopt the trigonal bipyramidal geometry, just as do the five bonding pairs of a PCl5 molecule or the two bonding and three non-bonding pairs of a XeF2 molecule. The molecular geometry of the former is also trigonal bipyramidal, whereas that of the latter is linear.
Possible geometries for steric numbers of 10, 11, 12, or 14 are bicapped square antiprismatic, octadecahedral, icosahedral, and bicapped hexagonal antiprismatic, respectively. No compounds with steric numbers this high involving monodentate ligands exist, and those involving multidentate ligands can often be analysed more simply as complexes with lower steric numbers when some multidentate ligands are treated as a unit.
Examples
The methane molecule is tetrahedral because there are four pairs of electrons. The four hydrogen atoms are positioned at the vertices of a tetrahedron, and the bond angle is cos−1 ≈ 109° 28′. This is referred to as an AX4 type of molecule. As mentioned above, A represents the central atom and X represents an outer atom.The ammonia molecule has three pairs of electrons involved in bonding, but there is a lone pair of electrons on the nitrogen atom. It is not bonded with another atom; however, it influences the overall shape through repulsions. As in methane above, there are four regions of electron density. Therefore, the overall orientation of the regions of electron density is tetrahedral. On the other hand, there are only three outer atoms. This is referred to as an AX3E type molecule because the lone pair is represented by an E. By definition, the molecular shape or geometry describes the geometric arrangement of the atomic nuclei only, which is trigonal-pyramidal for NH3.
Steric numbers of 7 or greater are possible, but are less common. The steric number of 7 occurs in iodine heptafluoride ; the base geometry for a steric number of 7 is pentagonal bipyramidal. The most common geometry for a steric number of 8 is a square antiprismatic geometry. Examples of this include the octacyanomolybdate and octafluorozirconate anions. The nonahydridorhenate ion in potassium nonahydridorhenate is a rare example of a compound with a steric number of 9, which has a tricapped trigonal prismatic geometry.
Exceptions
There are groups of compounds where VSEPR fails to predict the correct geometry.Some AX2E0 molecules
The shapes of heavier Group 14 element alkyne analogues have been computed to be bent.Some AX2E2 molecules
One example of the AX2E2 geometry is molecular lithium oxide, Li2O, a linear rather than bent structure, which is ascribed to its bonds being essentially ionic and the strong lithium-lithium repulsion that results. Another example is O2 with an Si–O–Si angle of 144.1°, which compares to the angles in Cl2O, 2O, and N3. Gillespie and Robinson rationalize the Si–O–Si bond angle based on the observed ability of a ligand's lone pair to most greatly repel other electron pairs when the ligand electronegativity is greater than or equal to that of the central atom. In O2, the central atom is more electronegative, and the lone pairs are less localized and more weakly repulsive. The larger Si–O–Si bond angle results from this and strong ligand-ligand repulsion by the relatively large -SiH3 ligand. Burford et al showed through X-ray diffraction studies that Cl3Al–O–PCl3 has a linear Al–O–P bond angle and is therefore a non-VSEPR molecule.Some AX6E1 and AX8E1 molecules
Some AX6E1 molecules, e.g. xenon hexafluoride and the Te and Bi anions,,,, and, are octahedra, rather than pentagonal pyramids, and the lone pair does not affect the geometry to the degree predicted by VSEPR. Similarly, the octafluoroxenate ion in nitrosonium octafluoroxenate is a square antiprism and not a bicapped trigonal prism, despite having a lone pair. One rationalization is that steric crowding of the ligands allows little or no room for the non-bonding lone pair; another rationalization is the inert pair effect.Transition metal molecules
Many transition metal compounds have unusual geometries, which can be ascribed to ligand bonding interaction with the d subshell and to absence of valence shell lone pairs. Gillespie suggested that this interaction can be weak or strong. Weak interaction is dealt with by the Kepert model, while strong interaction produces bonding pairs that also occupy the respective antipodal points of the sphere. This is similar to predictions based on sd hybrid orbitals using the VALBOND theory. The repulsion of these bidirectional bonding pairs leads to a different prediction of shapes.| Molecule type | Shape | Geometry | Examples |
| AX2 | Bent | ||
| AX3 | Trigonal pyramidal | CrO3 | |
| AX4 | Tetrahedral | TiCl4 | |
| AX5 | Square pyramidal | Ta5 | |
| AX6 | C3v Trigonal prismatic | W6 |
The Kepert model cannot explain the formation of square planar complexes.
Heavier alkaline earth halides
The gas phase structures of the triatomic halides of the heavier members of group 2,, are not linear as predicted but are bent,. It has been proposed by Gillespie that this is caused by interaction of the ligands with the electron core of the metal atom, polarising it so that the inner shell is not spherically symmetric, thus influencing the molecular geometry. Ab initio calculations have been cited to propose that contributions from the d subshell are responsible, together with the overlap of other orbitals.Odd-electron molecules
The VSEPR theory can be extended to molecules with an odd number of electrons by treating the unpaired electron as a "half electron pair" — for example, Gillespie and Nyholm suggested that the decrease in the bond angle in the series Nitronium ion|, NO2, Nitrite| indicates that a given set of bonding electron pairs exert a weaker repulsion on a single non-bonding electron than on a pair of non-bonding electrons. In effect, they considered nitrogen dioxide as an AX2E0.5 molecule, with a geometry intermediate between and. Similarly, chlorine dioxide is an AX2E1.5 molecule, with a geometry intermediate between Chloryl| and chlorite|.Finally, the methyl radical is predicted to be trigonal pyramidal like the methyl anion, but with a larger bond angle ). However, in this case, the VSEPR prediction is not quite true, as CH3 is actually planar, although its distortion to a pyramidal geometry requires very little energy.